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a: \(100+98+96+...+2-97-95-...-1\)
\(=100+\left(98-97\right)+\left(96-95\right)+...+\left(2-1\right)\)
\(=100+1+...+1\)
\(=100+49=149\)
b: \(1+2-3-4+5+6-7-8+9+10-11-12+...+...-299-300+301+302\)
\(=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(297+298-299-300\right)+603\)
\(=603+\left(-4\right)+\left(-4\right)+...+\left(-4\right)\)
\(=603-4\cdot75=603-300=303\)
a) 5 : 3/4 - 4 4/5 : 3/4
= 5 . 4/3 - 24/5 . 4/3
= (5 - 24/5) . 4/3
= 1/5 × 4/3
= 4/15
b) -3/5 . 2/7 + (-3/7) . 3/5 + (-3/7)
= (-3/7) . (2/5 + 3/5 + 1)
= (-3/7) . 2
= -6/7
c) [(-4 2/7) . 7/11 + 7/11 . (5 1/3)] . 5 - 5 2/3
= (-30/7 . 7/11 + 7/11 . 16/3) . 5 - 17/3
= (-30/11 + 112/33) . 5 - 17/3
= 2/3 . 5 - 17/3
= 10/3 - 17/3
= -7/3
d) 5/39 . [(7 4/5) . (1 2/3) + (8 1/3) . (7 4/5)]
= 5/39 . (39/5 . 5/3 + 25/3 . 39/5)
= 5/39 . 39/5 . (5/3 + 25/3)
= 1 . 10
= 10
=
a)x-5/7=-2/3+1/3
x-5/7=-1/3
x=-1/3+5/7
x=8/21
b)1/3x+5/7=-9/4
x+5/7=-9/4:1/3
x+5/7=-27/4
x=-27/4-5/7
x=-209/28
a: x-5/7=-2/3+1/3
=>x-5/7=-1/3
=>x=-1/3+5/7=8/21
b: 1/3*x+5/7=-9/4
=>x*1/3=-9/4-5/7=-83/28
=>x=-83/28:1/3=-83/28*3=-249/28
c: 1/6x:1/4=-1/24
=>1/6x=-1/96
=>x=-1/16
a: \(A=\dfrac{5}{7}-\dfrac{2}{7}+\dfrac{8}{11}+\dfrac{3}{11}+\dfrac{1}{2}=\dfrac{3}{7}+\dfrac{1}{2}+1=\dfrac{6+7+14}{14}=\dfrac{27}{14}\)
b: \(B=\dfrac{11}{17}+\dfrac{6}{17}-\dfrac{8}{19}-\dfrac{30}{19}+\dfrac{-3}{4}=1-2-\dfrac{3}{4}=-1-\dfrac{3}{4}=-\dfrac{7}{4}\)
c: \(C=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}=\dfrac{49}{50}\)
Bài 1:
a: \(\dfrac{25}{42}-\dfrac{20}{63}=\dfrac{75-40}{126}=\dfrac{35}{126}=\dfrac{5}{18}\)
b: \(\dfrac{9}{20}-\dfrac{13}{75}-\dfrac{1}{6}=\dfrac{135}{300}-\dfrac{52}{300}-\dfrac{50}{300}=\dfrac{33}{300}=\dfrac{11}{100}\)
- \(\dfrac{2}{5}\) + \(\dfrac{3}{-4}\) + \(\dfrac{6}{7}\) + \(\dfrac{3}{4}\) + \(\dfrac{2}{5}\)
= ( -\(\dfrac{2}{5}\) + \(\dfrac{2}{5}\))+ (- \(\dfrac{3}{4}\)+ \(\dfrac{3}{4}\)) + \(\dfrac{6}{7}\)
= 0 + 0 + \(\dfrac{6}{7}\)
= \(\dfrac{6}{7}\)